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Developing mathematical theories of the physical world: Open Access research on fluid dynamics from Strathclyde

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The gentle art of levitation

Chapman, James and Dagand, Pierre-Evariste and Mcbride, Conor and Morris, Peter (2010) The gentle art of levitation. In: ICFP 2010 Proceedings of the 15th ACM SIGPLAN international conference on functional programming. ACM, New York, NY, New York, pp. 3-14. ISBN 9781605587943

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Abstract

We present a closed dependent type theory whose inductive types are given not by a scheme for generative declarations, but by encoding in a universe. Each inductive datatype arises by interpreting its description - a first-class value in a datatype of descriptions. Moreover, the latter itself has a description. Datatype-generic programming thus becomes ordinary programming. We show some of the resulting generic operations and deploy them in particular, useful ways on the datatype of datatype descriptions itself. Simulations in existing systems suggest that this apparently self-supporting setup is achievable without paradox or infinite regress.